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Spin 1/2 in Modern QFT?

  1. May 17, 2015 #1


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    The spin observable for spin 1/2 particles is represented by Pauli Matrices acting upon a 2-dimensional Hilbert Space. In RQM, forgetting about the matter-antimatter duality for the moment, that TWO-state Hilbert Space is directly related, through the Lorentz Group, to the TWO separate differential equations in the Dirac Equation. Is that same "TWO-ness" also found in modern QFT for spin 1/2 particles? Are there TWO separate quantum fields for a spin 1/2 particle in modern QFT? As always, thanks in advance.
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  3. May 17, 2015 #2


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    The Dirac Equation holds in relativistic quantum field theory.
  4. May 19, 2015 #3


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    In addition one cannot stress early enough that a split of angular momentum in an orbital and a spin part is problematic in relativistic quantum field theory (to say the least). A thorough understanding of what's "spin" in relativistic QFT necessarily leads to Wigner's analysis of the irreducible unitary representations of the (quantum version of the) Poincare group. See

    Weinberg, S.: The Quantum Theory of Fields, volume 1, Cambridge University Press, 1995

    or my QFT lecture notes:

  5. May 19, 2015 #4
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